Semi-implicit high-order sliding mode control method for high dynamic servo system, medium and system

Abstract

The application relates to a semi-implicit high-order sliding mode control method, medium and system for a high dynamic servo system. The method comprises the following steps: adopting a sweep signal and a step signal to perform system identification on a linear motor, so as to construct a linear motor system model; replacing a position loop and a speed loop in an original three-loop PID in the system with a PSTA, and adopting a semi-implicit Euler discretization method for discretization; and compensating for a system disturbance term through a sliding mode observer method. The application can improve the control performance and stability of the system.

Description

TECHNICAL FIELD

[0001] The application relates to a semi-implicit high-order sliding mode control method, a medium and a system for a high dynamic servo system, and belongs to the field of servo system control. BACKGROUND

[0002] Permanent magnet synchronous linear motor (PMSLM) is a kind of motor that applies the principle of rotary motor to linear motion, and its working principle is similar to that of traditional permanent magnet synchronous motor, but its output is linear motion. The main features of permanent magnet synchronous linear motor include: the use of permanent magnets enables it to achieve a larger output force in a smaller volume; its compact structure enables it to respond quickly to input signals; and it has low noise and small vibration during operation. In high dynamic servo systems, permanent magnet synchronous linear motor is required to have high precision and high dynamic performance. For example, in industrial automation, robots and laser processing applications, the motor needs to be positioned with micron-level precision, and when starting and stopping quickly and turning, the motor needs to quickly adjust its motion state. And external interference factors have a significant impact on the performance of the motor, so it needs to have strong anti-interference ability. Therefore, the application of permanent magnet synchronous linear motor in high dynamic servo systems faces multiple challenges.

[0003] The current feedback controller can provide accurate positioning, has high robustness and external disturbance suppression effect when the PMSLM is in working condition change, and the mainstream three-loop PID control algorithm composed of position loop, speed loop and current loop in the market can perform well under ideal conditions. However, as the core driving device of high dynamic servo system, permanent magnet synchronous linear motor requires the control system to maintain stability and accuracy in a rapidly changing environment. However, in actual application, it often faces challenges such as external interference and load change, which not only affect the stability of the system, but also may cause the control accuracy to decrease, so it is particularly important to develop a new control algorithm.

[0004] With the increasing demand of manufacturing industry for high speed, high precision and high reliability, the traditional control algorithm has gradually shown its shortcomings. The existing PID (proportional-integral-derivative) control algorithm has the disadvantages of slow response speed and chattering phenomenon when facing complex dynamic systems, especially in high dynamic environment, the response speed of PID control is obviously insufficient, and due to the lack of robustness, it is easy to produce chattering when the load changes or external disturbance is large, and its design usually depends on accurate system model, when the model is inaccurate, the control effect will be significantly reduced. And some other modern control methods such as H∞ control and model predictive control (MPC) all require a large amount of calculation, which may cause response delay, and they are severely dependent on the mathematical model of the system, when the model is inaccurate, the control effect will be significantly reduced. SUMMARY

[0005] The application provides a semi-implicit high-order sliding mode control method, a medium and a system for a high dynamic servo system, aiming to at least solve one of the technical problems existing in the prior art.

[0006] The technical scheme of the application relates to a semi-implicit high-order sliding mode control method for a high dynamic servo system, and the method according to the application comprises the following steps:

[0007] S100, a sweep signal and a step signal are used to perform system identification on a linear motor to construct a linear motor system model;

[0008] S200, the position loop and the speed loop in the original three-loop PID of the system are replaced with a PSTA, and a semi-implicit Euler discretization method is used for discretization;

[0009] S300, a sliding mode observer is used to compensate for the system disturbance term.

[0010] Further, in the step S100, an equal-amplitude sinusoidal sweep signal is used, and the frequency thereof varies linearly with time; the sweep signal is represented as follows:

[0011] ,

[0012] In the formula, is a signal varying with time, is the amplitude of the signal, is the initial frequency, is the sweep rate, is time.

[0013] Further, in the step S100, the sweep signal is used as the reference signal of the current loop to model the linear motor; the linear motor system model obtained is represented as follows:

[0014] ,

[0015] In the formula, represents the transfer function model of the linear motor system, and s is a complex variable.

[0016] Further, in the step S200, the current loop transfer function is approximated as 1, and the load is regarded as a time-varying disturbance term to convert the system into a standard second-order system form, which is represented as follows:

[0017] ,

[0018] ,

[0019] ,

[0020] wherein, represents the linear motor position, represents the linear motor velocity, represents the drive quantity is saturated by the projection function proj(*), represents the maximum value of the drive quantity, represents the control quantity without saturation, , respectively represent the system model parameters, represents the external disturbance to the system.

[0021] Further, in the step S200, the PSTA controller is represented as follows:

[0022] ,

[0023] ,

[0024] ,

[0025] ,

[0026] ,

[0027] ,

[0028] wherein, represents the nonlinear terminal sliding mode surface, represents the tracking error, represents the convergence speed parameter of the error in the sliding mode surface, the operator sign represents , represents the parameter determining the convergence speed of the tracking error, represents the maximum value of the drive quantity; represents the sliding mode variable of the first-order terminal sliding mode control part; represents the sliding mode variable of the super-spiral control part; , represents the gain of the super-spiral control part; represents the equivalent control, represents the integral part of the super-spiral control.

[0029] Further, in the step S200, in the first stage of discretization of the PSTA controller, the first stage implicit Euler digital implementation of the PSTA controller is represented as follows:

[0030] ,

[0031] ,

[0032] wherein, denotes the value of the control variable at time tk+1h during the discretization process; denotes the value of the control variable at time tk+1h during the discretization process; denotes the value of the STA integral part at time tk+1h during the discretization process; ;

[0033] , , , denote intermediate variables, respectively, wherein,

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] wherein, denotes the sampling time interval, the index is the index of the time step, and ; , denote the value of the supercoiling control integral part and at time tk+1h during the discretization process, denote the value of the sliding mode variable of the supercoiling control part at time tk+1h during the discretization process; If

[0040] then:

[0041] ,

[0042] wherein is a single-valued sign function;

[0043] A digital implementation of the PSTA controller without any sign function can further be obtained and is represented as follows:

[0044] ,

[0045] ,

[0046] ​​where variables comprising and related predicted value.

[0047] Further, in the step S200, the PSTA controller is discretized in the second stage, and the attenuation term and is set as the disturbance term, and the combined disturbance is expressed as follows:

[0048] ,

[0049] and its derivative are expressed as follows:

[0050] ,

[0051] ,

[0052] ,

[0053] wherein, ;

[0054] using the nominal value of the input gain , the parameters , , the PSTA controller is discretized and implemented using the fully implicit Euler method, and the PSTA controller is expressed as follows:

[0055] ,

[0056] ,

[0057] ,

[0058] wherein, represents the value of the sliding mode variable of the super-helix control part at the time during discretization;

[0059] Further, using the semi-implicit Euler method for approximation, the PSTA controller is expressed as follows:

[0060] ,

[0061] ,

[0062] ,

[0063] , ​

[0064] ,

[0065] wherein, , ,

[0066] ,

[0067] ;

[0068] wherein, , , , respectively represent intermediate variables.

[0069] Further, in the step S200,

[0070] the load is regarded as a disturbance term, and a method of a sliding mode observer is used to estimate and compensate the above disturbance;

[0071] wherein, the sliding mode observer is expressed as follows:

[0072] ,

[0073] ,

[0074] ,

[0075] wherein,

[0076] ,

[0077] ,

[0078] ,

[0079] wherein, , , respectively represent correction terms of the observation , , ; represents a gain; , , respectively represent gains of the correction terms , , , represents a position error of the observer part.

[0080] The technical scheme of the present application also relates to a computer readable storage medium, which stores program instructions, and the program instructions are executed by a processor to implement the above method.

[0081] The technical scheme of the present application also relates to a semi-implicit high-order sliding mode control system for a high dynamic servo system, which comprises a computer device containing the above computer readable storage medium.

[0082] The present application has the following beneficial effects:

[0083] The semi-implicit high-order sliding mode control method, medium and system for a high dynamic servo system of the present application aim to solve the technical problems of insufficient control precision, delayed response time and weak robustness to external interference in a high dynamic servo system, and the proposed semi-implicit high-order sliding mode control algorithm can improve the control performance and stability of the system. The present application uses the least square method to establish a mathematical model of a permanent magnet synchronous linear motor, proposes a discrete high-order sliding mode control algorithm Proxy-based Super-Twisting Algorithm (PSTA) based on a semi-implicit Euler discretization method, uses the PSTA to replace the position loop and speed loop in the original three-loop PID controller, and applies it to a permanent magnet synchronous linear motor system.

[0084] For a permanent magnet synchronous linear motor, the motion mode is analyzed, a typical motion mode model is established, current mainstream PMSLM control algorithms are analyzed, and a high-robustness micro-mirror control algorithm meeting the requirements is designed according to the MEMS motion model, the position of the PMSLM is controlled, accurate tracking of the input signal is realized, finally, the accuracy, robustness and other evaluation indexes of the controller are established, and the superiority of the proposed control algorithm is verified on a PMSLM test platform. BRIEF DESCRIPTION OF DRAWINGS

[0085] Figure 1 It is a control system block diagram of a permanent magnet synchronous linear motor according to the method of the present application.

[0086] Figure 2 It is a sweep signal curve with an amplitude of 7 of a permanent magnet synchronous linear motor according to the method of the present application.

[0087] Figure 3 It is a block diagram of a traditional three-loop PID control algorithm. DETAILED DESCRIPTION

[0088] The concept, specific structure and generated technical effects of the present application will be described clearly and completely in the following combined with embodiments and drawings, so as to fully understand the purpose, scheme and effect of the present application.

[0089] It should be noted that, unless otherwise specified, when a certain feature is termed "fixed", "connected" to another feature, it can be directly fixed, connected to the other feature, or indirectly fixed, connected to the other feature. The singular forms "a", "said" and "the" used in this document are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used in this document have the same meaning as understood by those skilled in the art. The terms used in the specification herein are only for the purpose of describing specific embodiments and are not intended to limit the present application. The term "and / or" used herein includes any combination of one or more related listed items.

[0090] It should be understood that, although the terms first, second, third, etc. can be employed in this disclosure to describe various elements, these elements should not be limited to these terms. These terms are only used to distinguish one type of element from another type of element. For example, a first element can also be referred to as a second element, and similarly, a second element can also be referred to as a first element, without departing from the scope of the present disclosure. The use of any and all examples, or exemplary language ("for example", "for instance", etc.) provided herein is intended merely to better illuminate the embodiments of the present application and does not impose a limitation on the scope of the present application, unless otherwise required.

[0091] Referring to Figures 1 to 2 In some embodiments, the semi-implicit high-order sliding mode control method for high dynamic servo system according to the present application comprises at least the following steps:

[0092] S100, system identification is performed on the linear motor using a sweep signal and a step signal to construct a linear motor system model;

[0093] S200, the position loop and the speed loop in the original three-loop PID of the system are replaced by PSTA, and semi-discretization is performed based on the semi-implicit Euler discretization method;

[0094] S300, the system disturbance term is compensated by the method of the sliding mode observer.

[0095] The present application realizes the super-spiral control algorithm (high-order sliding mode control algorithm) based on semi-implicit Euler discretization on a high dynamic servo control system, and improves the control precision. The super-spiral controller based on agent designed by semi-implicit Euler method is applied to the control of PMLSM, and is applied to the controller of the actual PMLSM system, which effectively improves the control precision, and proves the superiority of the control system through practice.

[0096] The method can be applied to a motion platform based on a permanent magnet synchronous linear motor, and specifically, the motion platform comprises a sliding table, a linear motor platform, a resistor and a driver, the driver is connected with the resistor, the sliding table is driven by the linear motor platform to perform linear motion, and a semi-implicit high-order sliding mode control system controls the linear motor platform through the driver.

[0097] In some embodiments, the permanent magnet synchronous linear motor system to which the application is directed belongs to the characteristics of a linear system, and a sweep signal and a step signal are used for system identification of the linear motor. The sweep signal has a wide frequency coverage range, can excite various frequency components of the system, and obtain the frequency response characteristics of the system, but the measurement time of the sweep signal is relatively long, especially in the low frequency band, a long sweep is required, while the step signal is simple and easy to implement, can quickly excite the transient response of the system, but cannot excite all frequency components of the system.

[0098] It can be understood that in the permanent magnet synchronous linear motor model of the application, the target of system identification is to determine the mathematical model of the system according to experimental data, which usually includes four steps of data collection, model selection, parameter estimation and model verification. In system identification, there are various excitation signals to choose from, including step signals, pulse signals, sweep signals, sine wave signals, square wave signals, etc. Selecting a suitable excitation signal needs to consider the linear and nonlinear characteristics of the system, the limitations of experimental equipment and conditions, and the working frequency range of the system, etc.

[0099] In an application embodiment, the sweep signal uses equal-amplitude sinusoidal sweep, and the frequency changes linearly with time. The sweep signal is expressed as follows:

[0100] ;

[0101] In the formula, is a signal that changes with time, is the amplitude of the signal, is the initial frequency, is the sweep rate, is the time.

[0102] Further, the application uses three groups of sweep signals with different amplitudes for verification, and the three groups of amplitudes are 5, 7 and 10 respectively, wherein the starting frequency of each group of signals is 1 Hz, the cutoff frequency is 25 Hz, and the sweep rate is 5, as shown in the sweep signal curve with an amplitude of 7. Figure 2

[0103] The application uses the sweep signal as the reference signal of the current loop, collects experimental data, and uses the system identification toolbox of Matlab to process and analyze the data to accurately model the linear motor. The linear motor system model obtained by modeling is expressed as follows:​

[0104] ;

[0105] wherein, represents the transfer function model of the linear motor system, which is converted from the time domain to the frequency domain by a complex variable s, and is used to analyze the stability, frequency response and dynamic characteristics of the system.

[0106] In an application embodiment, the present application replaces the position loop and the speed loop in the original three-loop PID of the system with a PSTA, and approximates the transfer function of the current loop to 1, and regards the load as a time-varying disturbance term , so as to convert the system into a standard second-order system form:

[0107] ,

[0108] ,

[0109] ,

[0110] wherein, represents the position of the linear motor, represents the speed of the linear motor, represents the driving quantity subjected to the saturation limitation of the projection function proj (*), represents the maximum value of the driving quantity, represents the control quantity not subjected to the saturation limitation, , represents the model parameters of the system, represents the external disturbance to which the system is subjected.

[0111] In some embodiments, the PSTA controller of the present application is represented as follows:

[0112] ,

[0113] ,

[0114] ,

[0115] ,

[0116] ,

[0117] ,

[0118] wherein, represents a nonlinear terminal sliding surface, represents a tracking error, represents a convergence speed parameter of the error in the sliding surface, and the operator sign express , This represents the parameter that determines the convergence rate of the tracking error. Indicates the maximum value of the driving quantity; Represents the sliding mode variable of the first-order terminal sliding mode control part; Represents the sliding mode variable of the superspiral control section; , This indicates the gain of the superspiral control section; Indicates equivalent control. This represents the integral part of the superspin control.

[0119] In some application embodiments, the present invention is implemented in the first stage of PSTA controller discretization, namely... or At that time, the original system was a first-order disturbed dynamic system controlled by a first-order sliding mode controller. Therefore, the PSTA controller is an algebraic inclusion relation, which cannot be directly implemented due to the existence of set-valued sign functions. To obtain a discretized controller, this invention first sets... Available, and Known. Then, eliminate by rewriting the system. It is represented as follows:

[0120] ,

[0121] ,

[0122] Wherein, the above formula is about the sliding mode variable. An algebraic inclusion relation. Discretized using the implicit Euler method, it can be represented as follows:

[0123] ,

[0124] ,

[0125] In the formula, Indicates the sampling time interval, index. It is the index of the time step, i.e. and ; , These represent the discretization process. and Integral part of time-of-flight superspin control The value, Represents the discretization process Sliding mode variable of the time-lapse superspin control section The value, Represents the discretization process Time-Nonlinear Terminal Sliding Surface the value of the tracking error at time

[0126] Substituting into the above equation, we have the following expression:

[0127] ,

[0128] The above equation is equivalent to the following expression:

[0129] ,

[0130] where represents the value of the tracking error at time during the discretization process.

[0131] Due to the property , , , we can determine appropriate choices of and such that is satisfied, and we have:

[0132] ,

[0133] where , , , represents an intermediate variable, where

[0134] ,

[0135] ,

[0136] ,

[0137] ,

[0138] .

[0139] Thus, the update law for is given by:

[0140] ,

[0141] where is a single-valued sign function. Due to , the first stage of the implicit Euler digital implementation formula for the PSTA controller is given by:

[0142] ,

[0143] ​,

[0144] Represents the discretization process The value of the control quantity is controlled at all times.

[0145] Therefore, it can be concluded that the symbolic function "" still exists in the formula. The existing direct method is to use single-valued symbolic functions. To approximate it. However, to avoid numerical jitter caused by single-valued sign functions, the present invention can also employ another method: if Then we have:

[0146] ,

[0147] Finally, this invention yields a digital implementation scheme for the PSTA controller without any sign function, as shown below:

[0148] ,

[0149] ,

[0150] In the formula, variables Includes and Related The predicted value can be accurately predicted using an observer.

[0151] In some application embodiments, in the second stage of PSTA controller discretization, based on the analysis of the first stage, at this time... and Among them, the attenuation term It is represented as follows,

[0152] ,

[0153] In the formula, This represents the parameter that determines the convergence speed of the tracking error.

[0154] The system controlled by the PSTA controller is actually a disturbed first-order dynamic system controlled by the STA, with an input gain of... Therefore, in the second stage, the performance of the PSTA controller, such as control accuracy and convergence, is ultimately determined by the accuracy of the STA.

[0155] To obtain the discrete-time implementation algorithm for the second stage, and for simplicity, this invention will use the attenuation term. and Considered as interference, i.e., interference after merging. It is expressed as follows:

[0156] ,

[0157] and its derivative are given by

[0158] ;

[0159] ,

[0160] ,

[0161] where the nominal value of the input gain is used by choosing the parameter , The PSTA controller is discretized and implemented using the fully implicit Euler method, whose specific method is given by

[0162] ,

[0163] ,

[0164] ,

[0165] where denotes the value of the sliding mode variable of the supercoiling control part at time .

[0166] It should be noted that the discretization of the disturbance term and its derivative does not mean that and are piecewise constants, but it means that they have no effect on in the time period after being sampled by the analog-to-digital conversion (ADC) device at time .

[0167] Further, the semi-implicit Euler method is used to approximate

[0168] ,

[0169] ,

[0170] ,

[0171] ,

[0172] ,

[0173] where , ,

[0174] ,

[0175] ;

[0176] wherein, , , , respectively represent intermediate variables.

[0177] Thus, the discrete-time implementation method of the PSTA control algorithm in the second stage of the present application can be obtained.

[0178] In some embodiments, in the implementation of the observer, in order to improve the steady-state accuracy and response speed of the closed-loop control system, the load is regarded as a disturbance term, and the observer method is used to estimate and compensate for such disturbance, thereby improving the response speed and control accuracy of the system. With the increase of the load, the effect of the observer will become more significant. The sliding mode observer is a kind of nonlinear observer, and compared with the Luenberger observer, its variable gain characteristic makes the convergence speed faster. The sliding mode observer of the present application is represented as follows:

[0179] ,

[0180] ,

[0181] ,

[0182] wherein,

[0183] ,

[0184] ,

[0185] ,

[0186] wherein, , , respectively represent correction terms of the observed variables , , ; represents a gain; represents a measured value; , , respectively represent gains of the correction terms , , , represents a position error of the observer part.

[0187] Finally, the control system block diagram of the application is shown in Figure 1 .

[0188] It can be understood that, referring to Figure 3 , the existing three-ring PID control algorithm is composed of three parts: position loop, speed loop and current loop, which improves the system response speed and steady-state accuracy through hierarchical control. Among them, the position loop is responsible for converting the set target position into the target speed, calculating the error between the set position and the actual position, and generating the target speed using the PID controller. The speed loop converts the target speed into the target current, calculates the speed error and adjusts the current to meet the dynamic demand. The current loop directly controls the motor current, calculates the driving signal through the current error, and realizes fast response. In general, the three-ring PID control algorithm provides an effective control scheme for permanent magnet synchronous linear motor, which realizes high precision and high dynamic performance through hierarchical control. However, although the three-ring PID control can perform well under ideal conditions, as the core driving device of high dynamic servo system, permanent magnet synchronous linear motor requires the control system to maintain stability and accuracy in rapidly changing environment. In actual application, it often faces challenges such as external disturbance and load change. These factors not only affect the stability of the system, but also may cause the control accuracy to decrease. Therefore, it is particularly important to develop new control algorithm.

[0189] Compared with traditional PID control, H∞ control and model predictive control, the sliding mode control adopted by the application has better adaptability and performance in high dynamic servo system, and becomes an ideal choice to realize high precision and high dynamic control. Among them, sliding mode control as a nonlinear control strategy, shows significant advantages in high dynamic servo system. Sliding mode control has strong anti-interference ability to system uncertainty and external disturbance, and can guarantee the stability in complex dynamic environment. At the same time, sliding mode control can quickly guide the system state to the sliding mode surface, so as to realize fast response, which is suitable for high dynamic application. By designing the sliding mode surface, sliding mode control effectively suppresses the chattering phenomenon that may occur in the control process, and improves the stability and accuracy of the system. In addition, sliding mode control has low dependence on the model of the controlled object, and can still maintain effective control in the absence of accurate model, thereby enhancing the flexibility of the system.

[0190] It should be noted that the sliding mode control, due to its robustness and insensitivity to parameter disturbances, has shown significant advantages in the demand of high dynamic servo systems. First, the high-order sliding mode control algorithm can effectively handle the uncertainty and external disturbances of the system, thereby ensuring the rapid adaptation to the load changes. This feature enables the permanent magnet synchronous linear motor to maintain high-precision positioning in complex environments. In addition, the algorithm can quickly guide the system state to the desired trajectory by designing a high-order sliding surface, significantly improving the response speed of the system. This fast response capability is crucial to meet the requirements of high dynamic applications. High-order sliding mode control can also effectively suppress the chattering phenomenon that may occur during control, ensuring the smoothness and accuracy of the motor during high-speed motion, thereby further improving the performance of the system. Moreover, the high-order sliding mode control algorithm reduces the dependence on the accurate model parameters of the controlled object, making the control system more flexible and suitable for various working conditions. This model-independent feature enables the sliding mode control to have stronger adaptability in a variable environment.

[0191] Therefore, the demand for high precision and high dynamic performance of the permanent magnet synchronous linear motor in high dynamic servo systems fully demonstrates the advantages of the high-order sliding mode control algorithm in improving the performance of the system. The semi-implicit high-order sliding mode control algorithm of the present application provides strong support for the application of high-efficiency automated servo systems, which not only proves the feasibility of the control system in theory, but also improves the practical application according to the physical control, giving a feasible scheme for practical application, which can effectively improve the control precision of the PMSLM and reduce the cost of the equipment.

[0192] It should be recognized that the method steps in the embodiments of the present application can be realized or implemented by computer hardware, a combination of hardware and software, or through computer instructions stored in a non-transitory computer readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, the program can run on a programmed special-purpose integrated circuit for this purpose.

[0193] In addition, the operations of the processes described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) can be performed under the control of one or more computer systems configured with executable instructions (e.g., executable instructions, one or more computer programs, or one or more applications) to perform the processes, and can be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) executing collectively on one or more processors, by hardware, or combinations thereof. The computer programs include a plurality of instructions executable by one or more processors.

[0194] Further, the methods can be implemented in any type of computing platform operably connected to a suitable computing platform, including but not limited to a personal computer, mini-computer, mainframe, workstation, network or distributed computing environment, separate or integrated computer platforms, or in communication with charged particle tools or other imaging devices, and the like. Aspects of the present application can be implemented in machine readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage media, RSM, ROM, and the like, such that it can be read by a programmable computer to configure and operate the computer to perform the processes described herein when the storage medium or device is read by the computer. In addition, the machine readable code, or portions thereof, can be transmitted over wired or wireless networks. The present application described herein includes these and other different types of non-transitory computer readable storage media when such media include instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. The present application can also include the computer itself when programmed in accordance with the methods and techniques described herein.

[0195] The computer program can be applied to input data to perform the functions described herein to transform the input data to generate output data that is stored to non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present application, the transformed data represents a physical and tangible object, including a particular visual depiction of the physical and tangible object produced on a display.

[0196] The above description is only preferred embodiments of the present application, and the present application is not limited to the above-described embodiments, but any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the present application. The technical solutions and / or embodiments of the present application can have various modifications and changes within the scope of the present application.

Claims

1. A semi-implicit higher order sliding mode control method for high dynamic servo systems, characterized in that, The method comprises the following steps: S100, system identification is performed on the linear motor using a sweep signal and a step signal to construct a linear motor system model; S200, the position loop and the speed loop in the original three-loop PID of the system are replaced by a PSTA, and a semi-implicit Euler discretization method is used for discretization; S300, the system disturbance term is compensated by a sliding mode observer method; In the step S200, the current loop transfer function is approximated as 1, and the load is regarded as a time-varying disturbance term to transform the system into a standard second-order system form, which is expressed as follows: ， ， ， wherein, represents the linear motor position, represents the linear motor velocity, represents the drive quantity subjected to a projection function saturation limitation, represents the maximum value of the drive quantity, represents the control quantity not subjected to the saturation limitation, , respectively represent system model parameters, represents an external disturbance to which the system is subjected; In the step S200, the control of the PSTA is represented as follows: ， ， ， ， ， ， wherein denotes a nonlinear terminal sliding surface, denotes a tracking error, denotes a convergence speed parameter of the error in the sliding surface, and the operator denotes , denotes a parameter that determines the convergence speed of the tracking error, , denotes a maximum value of the driving amount; denotes a sliding variable of a first-order terminal sliding mode control part; denotes a sliding variable of a super-spiral control part; , denotes a gain of the super-spiral control part; denotes an equivalent control, denotes an integral part of the super-spiral control; In the step S200, in the first stage of the discretization of the PSTA controller, the first-stage implicit Euler digital implementation of the PSTA controller is represented as follows: , ， wherein represents the value of the control variable at time t = kh during the discretization process represents the value of the control variable at time t = kh during the discretization process represents the value of the control variable at time t = kh during the discretization process ; , , , denote intermediate variables, respectively, wherein, ； ； ； ； ； wherein, denotes the sampling time interval, the index is the index of the time step, and ; , denote the values of the and integral part of the hyper-super-twisting control at the time instant , denote the values of the sliding variable of the hyper-super-twisting control part at the time instant , ; denotes the value of the nonlinear terminal sliding surface at the time instant ; Let , then we have: ， In the formula is a single-valued sign function; Further, the digital implementation scheme of the PSTA controller without any symbolic function is obtained, which is represented as follows: ， ， In the formula, the variables comprising and related to the predicted value.

2. The method of claim 1, wherein, In the step S100, an equal-amplitude sinusoidal sweep signal is used, and the frequency thereof varies linearly with time; the sweep signal is represented as follows: ， In the formula, x(t) is a signal varying with time, A is the amplitude of the signal, f0 is the initial frequency, k is the sweep rate, and t is time.

3. The method of claim 2, wherein, In the step S100, the sweep signal is used as the reference signal of the current loop to model the linear motor; the obtained linear motor system model is represented as follows: ， In the formula, represents the transfer function model of the linear motor system, and s is a complex variable.

4. The method of claim 1, wherein, In the step S200, in the second stage of PSTA controller discretization, the attenuation term and is set as the interference term, and the combined interference is represented as follows: ， The derivative thereof is represented as follows: ， ， ， wherein ; Using nominal values of input gains , selecting parameters , , using a fully implicit Euler method for discretization and implementation of the PSTA controller, the PSTA controller can be represented as follows: ， ， In the formula, represents the value of the sliding mode variable of the super-spiral control part in the discretization process the value of the sliding mode variable of the super-spiral control part in the discretization process​ Then, the semi-implicit Euler method is used for approximation, and the PSTA controller is obtained and represented as follows: ， ， ， ， ， wherein , , ， ； wherein , , , respectively represent intermediate variables.

5. The method of claim 4, wherein, In the step S200, The load is set as the disturbance term, and the sliding mode observer method is used to estimate and compensate the disturbance; The sliding mode observer is represented as follows: ， ， ， Wherein, ， ， ， wherein , , respectively represent correction terms for the observation , , ; represents a gain; , , respectively represent correction terms , , for the gain of the correction terms, represents a position error of the observer part.

6. A computer readable storage medium characterized by The program instructions are stored in the computer readable storage medium, and the program instructions are executed by the processor to implement the method in any one of claims 1 to 5.

7. A semi-implicit higher order sliding mode control system for high dynamic servo systems, characterized by, Comprise: The computer device comprises the computer readable storage medium according to claim 6.

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